【作者】 李珊珊；

【导师】 康志伟；

【作者基本信息】 湖南大学 ， 通信与信息系统， 2006， 硕士

【摘要】 小波滤波器是小波分析理论在实际工程应用中的重要工具。随着小波变换在模式识别、图像压缩、语音编码和信息隐藏等方面的广泛应用，小波滤波器设计成为了近年来小波理论研究中一个重要的研究领域。尤其是在图像及信号压缩方面，小波变换以其优越的时频分析特性，逐渐取代了传统的DCT变换。但是，由于小波理论产生的时间不长，小波滤波器的设计还存在许多需要完善的地方。因此，本文首先分析了小波滤波器设计的基本方法，在此基础上，对图像及信号处理中最常用的双正交小波滤波器组进行了深入研究及改进。本文主要工作如下：(1)深入研究小波变换理论和小波滤波器设计的基本方法。(2)针对CDF9／7小波系数为无理数的缺点，对CDF9／7小波滤波器组的完全重构条件和双正交条件进行三角基函数变换和因式分解，并对求出的小波滤波器系数进行优化设计，得到一组滤波器系数都为二进制分数的9／7双正交小波滤波器组，大大降低了离散小波变换的算法复杂度。(3) EBFB小波滤波器是基于伯恩斯坦多项式的偶数长双正交小波滤波器组，本文针对伯恩斯坦多项式中参数的不确定性，提出了一种基于遗传算法的EBFB双正交小波滤波器组的优化设计方法。通过实验证明了该小波滤波器具有更好的幅频特性。(4)为了获得信号的最优小波变换，本文在双正交小波滤波器组系数有理化的基础上，根据输入信号在尺度空间的最大投影原则，选择信号小波变换后低频部分的能量与总能量的比值为优化的目标函数，设计了一种适用于信号压缩的匹配小波滤波器并给出了具体的应用实例。本文利用MATLAB7.0作为仿真实验平台，将设计出的小波滤波器具体应用于图像与信号压缩中，验证和分析了所得滤波器组的优良特性。更多还原

【Abstract】 The wavelet filter is a important tool for the wavelet analysis theory in the actual project application. Along with the widespread applications of wavelet transform in pattern recognition, image compression, pronunciation code and information hideaway, the wavelet filter design become more and more important in recent years. Especially in the compression of image and signal, the wavelet transform will substitute for the traditional DCT transform by its superior time frequency analysis characteristic. However, the theory of wavelet is very short since wavelet was put forward, so the wavelet filter design still has many problems need to consummate. Therefore, this article has analyzed the essential method of the wavelet filter design, in this foundation, we have research and improve thoroughly the biorthogonal wavelet filter group which are used most commonly in the process of image and signal.The main important work of this paper:1. Deeply studied wavelet analysis theory and wavelet filter banks design technology.2. In view of the coefficients of CDF9/7 wavelet filter are irrational number, we use the trigonometric function transform to factorize the perfect restruction and the biorthogonal conditions of biorthogonal wavelets filter banks, then optimize the coefficients of the original 9/7 wavelet filter banks, consequently a novel 9/7 wavelet filter banks with binary digit coefficients can be obtained. This arithmetic can reduce the complexity greatly.3. EBFB was a new class of even-length biorthorgonal wavelet filter banks base on Parametric Bernstein. Due to the uncertainty of parameters of the Bernstein Polynomial, a design method for optimizing EBFB filter banks based on genetic algorithms was presented. The experimental result shows that the new filter banks have better amplitude-frequency characteristic.4. To obtain the best wavelet transform of a given signal, the paper propose a method which choose the ratio energy of low-frequency domain to total signal as objective function to optimize the uncertain parameters in filter coefficients based on rationalizing the coefficients of popular biorthogonal wavelet filters and the criterion that maximizing the projection of a signal onto the scale subspace. Then we can get amatching wavelet filter which is suitable in signal compression. Correspondingly, we have given the concrete example.We used MATLAB7.0 as the simulation platform, apply the wavelet filter above in the compression of signal and image, confirm and analyze the obtained fine characteristic of wavelet filter banks.更多还原